Symmetries of crystallographic groups

by Prof. Andrzej SZCZEPANSKI (University of Gdansk & IHES)

Tuesday Feb 9, 2016, 2:30 PM → 3:30 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Let G be a crystallographic group of dimension n, i.e. a discrete, cocompact subgroup of Isom(R^n) = O(n) \ltimes R^n. By symmetries of G we understand a group Out(G). For any n ≥ 2, we shall construct a crystallographic group with trivial center and a trivial outer automorphism group. Moreover, we shall present properties of an example (constructed by R. Waldmuler in 2003) of the torsion free crystallographic group of dimension 141 with a trivial center and a trivial outer automorphism group. (It is a joint work with R. Lutowski.)